Signal amplitude distribution analyzer

ABSTRACT

A signal amplitude distribution analyzer measures the amplitude probability density function of electrical signals, and in particular, the amplitude probability distribution of noise signals. Such measurements may be used to determine the &#34;Gaussianicity&#34; of noise signals, that is, a measurement of how closely the amplitude distribution of noise signals corresponds to theoretical values derived from the Gaussian probability distribution density function. This theoretical density function represents the relative percentage of time that a noise signal is at a given amplitude. The invention gives an approximation of this function by measuring the amount of time a noise signal is between a window of two adjustable voltage levels. This is accomplished by producing an output voltage proportional to the amount of time a noise signal amplitude falls within the window of values defined by the two adjustable voltage levels. The center point of this window is then plotted versus the invention&#39;s output voltage, giving the amplitude distribution density. This is then compared to the theoretical density function, plotted on the same graph, to determine signal &#34;Gaussianicity.&#34; The invention is calibrated to give an output that is Gaussian when analyzing a known Gaussian input. A continuous resolution measurement of the signal amplitude probability density function is possible, permitting accurate analysis of noise statistics in terms of skewness, clipping, etc. The cumulative amplitude distribution of noise signals can also be measured by the analyzer of the invention.

STATEMENT OF GOVERNMENT INTEREST

The invention described herein may be manufactured and used by or forthe Government of the United States of America for governmental purposeswithout the payment of any royalties thereon or therefor.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates generally to the field of signal analyzers and,more particularly, to a signal analyzer designed to measure theamplitude probability distribution of electrical signals. In greaterparticularity, the invention relates to a signal analyzer designed tomeasure the amplitude probability density function of noise signals toallow characterization of the signal's statistics in terms of skewness,clipping, kurtosis and other non-Gaussian deviations.

2. Description of the Related Art

In the past, the Gaussianicity of noise signals was estimated bymeasuring the signal's cumulative amplitude distribution. Thismeasurement was done through repetitive sampling of signal amplitude incombination with computer analysis, or by a simple comparator circuitsuch as that described on pages 272-274 of the Dec. 11, 1986 EDNmagazine article titled, "Test whether a noise source is Gaussian."

The cumulative amplitude distribution function gives the probabilitythat a variable will assume a value equal to or greater than aparticular value over a range of values. By the cumulative amplitudedistribution method, the relative Gaussianicity of noise signals isdetermined by the degree of conformance of measured data to atheoretical cumulative distribution curve.

A limitation of the cumulative amplitude distribution method is thatmeasured data do not show the actual distribution of amplitudes. Becauseof this, departures of data from the theoretical curve do notcharacterize precisely how a noise signal is different from trueGaussian noise. As will be visually depicted in this disclosure, thismethod indicates non-Gaussianicity only by a departure of the signal'splotted distribution from the theoretical cumulative amplitudedistribution curve. Abnormal characteristics of the noise signal such asskewness, kurtosis, clipping and other non-Gaussian deviations cannot bereadily identified.

The cumulative amplitude distribution method can also be relativelyinsensitive and give results that are difficult to relate to in Gaussianterms, thereby making it difficult to judge the overall degree ofnon-Gaussianicity of noise signals.

Another probability distribution is the amplitude probability densitydistribution. This distribution gives the probability that a variablewill assume a value near any particular value in its range of values.

Techniques exist for calculating amplitude probability densitydistributions. One such technique is described in U.S. Pat. No.3,626,168 issued to Keith H. Norsworthy. This patent describes aninvention capable of a multitude of signal measurements. Formeasurements of amplitude probability density distribution, thisinvention outputs an indicating signal when an input signal fallsbetween two known signal levels. The indicating signal is thenapparently sent to an averaging bin to provide a digitally constructeddensity distribution. The '168 patent describes an invention that ishighly complex and because of the use of a finite number of averagingbins, it cannot provide continuous resolution capability.

In a second scheme, the amplitude probability density distribution isdetermined through an invention described in U.S. Pat. No. 3,581,200.This invention produces a probability density function profile throughthe use of a wave generator, spectrum analyzer, sweep generator and x-yrecorder. The '200 invention converts signal amplitude distributionsinto a frequency domain profile for visualization by way of the spectrumanalyzer. The invention is of relative high complexity, and nature ofthe design appears to make system calibration difficult.

In a related but different area, the invention of U.S. Pat. No.4,625,283 issued to James R. Hurley describes an invention designed toanalyze repetitive signals, e.g. sinewave signals. This inventionmeasures the elapsed times it takes for an alternating current signal tocross predetermined reference values and compares these with knownvalues to determine characteristics of an alternating current signalbeing analyzed. Signal characteristics such as frequency, size of directcurrent offset and waveform amplitude apparently can be determined withthis invention.

A need thus exists for a simple, calibrated device that permitscontinuous resolution of signal amplitude probability distribution. Suchan invention should be able to readily permit the perception of noisesignal skewness, kurtosis, clipping, as well as other non-Gaussiandeviations.

SUMMARY OF THE INVENTION

The signal amplitude distribution analyzer of the invention is designedto measure the amplitude probability density function of electricalsignals. This invention has been particularly devised to measure theamplitude probability distribution of noise signals. Such measurementsmay be used to determine the "Gaussianicity" of noise signals, that is,a measurement of how closely the amplitude density distribution of noisesignals corresponds to theoretical values derived from the Gaussianprobability density distribution function (i.e. a normal distributioncurve). This theoretical density function represents the relativepercentage of time that a noise signal is at a given amplitude. Theinvention gives an approximation of this function by measuring theamount of time a noise signal is between a window of two adjustablevoltage levels. This is accomplished by producing an output voltageproportional to the amount of time a noise signal amplitude falls withinthe window of values defined by the two adjustable voltage levels. Bothrepetitive and non-repetitive signals may be measured.

The center point of the window is then plotted versus the invention'soutput voltage, giving the amplitude distribution density. This is thencompared to the theoretical density function, plotted on the same graph,to determine signal "Gaussianicity." The invention is calibrated to givean output that is Gaussian when analyzing a known Gaussian input. Acontinuous resolution measurement of the signal amplitude probabilitydensity function is possible, permitting accurate analysis of noisestatistics in terms of skewness, clipping, etc. The cumulative amplitudedistribution of noise signals can also be measured.

OBJECTS OF THE INVENTION

It is an object of this invention is to provide an improved signalanalyzer.

Another object of this invention is to provide an improved signalanalyzer that is simple in operation.

Yet another object of this invention is to provide an improved signalanalyzer that is capable of continuous resolution.

A further object of this invention is to provide an improved signalanalyzer that may be easily calibrated so as to provide a quantitativemeasurement.

Still a further object of this invention is to provide an improvedsignal analyzer that measures amplitude probability densityfunctions/probability density distributions.

Other objects, advantages and new features of the invention will becomeapparent from the following detailed description of the invention whenconsidered in conjunction with the accompanied drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic of a representative embodiment of the signalamplitude distribution analyzer of the invention.

FIG. 2 depicts waveforms useful in describing the calibration procedureof the invention.

In FIG. 3 there are plotted outputs of the invention as compared to atheoretically derived signal amplitude probability density distributionand a cumulative amplitude distribution.

DESCRIPTION OF THE PREFERRED EMBODIMENT

Referring now to FIG. 1 a schematic diagram of signal amplitudedistribution analyzer 10 is shown. In the representative embodiment ofthe invention shown, all resistors are in ohms and capacitors are inmicrofarads (μF). All 3 integrated circuit (IC) power connections aredecoupled by 100 ohm, and 0.1 μF filter networks. In FIG. 1 resistor R1provides a 50-ohm termination for signal source 12 being tested. Thesource is fed as an input signal, V_(in), that is then connected to aninverting input of integrated circuit 1 (ICl), pin 4, and thenon-inverting input of IC2 (pin 3) through isolating resistors R2 andR3, respectively. Integrated circuits IC1 and IC2 are high speedcomparators such as LM361s. The reference voltage for IC1 and IC2,V_(x), about which a noise signal is analyzed, is set by resistors R4,R5 and R6, and is applied to pins 3 and 4 of IC1 and IC2, respectively.Capacitor C1 provides filtering so that V_(x) remains at the voltage setby R5 in spite of any feedback of comparator switching transients. Theother inputs to IC1 and IC2 are variable voltages that compensate for ICoffset voltages and currents, and also set comparator thresholds. Thevoltage (V_(H)) at pin 4 of ICl is primarily determined by a voltagedivider including R9, R10, R2, R1 and the signal source resistance. Thevoltage (V_(L)) at pin 3 of IC2 is developed similarly by R7, R8, R3, R1and the signal source resistance.

Referring now to FIGS. 1 and 2, the voltage at pin 4 of IC1 (V_(H)) isnormally set to some small negative voltage and that at pin 3 of IC2(V_(L)) to a small positive voltage creating a preselected "window" ofvoltage levels. With V_(x) set for 0 volts DC (VDC), then, when V_(in)is very negative, IC1 output will be high (positive) and IC2 will be low(nominally zero volts). IC1 and IC2 outputs are applied to pins 1 and 2of an AND gate IC3, such as a 74HC08, the output at pin 3 of which willthus be low. When V_(in) rises to a negative voltage slightly smallerthan the positive bias at pin 3 of IC2, pin 3 becomes positive withrespect to pin 4 and IC2 goes high. Both inputs to IC3 are then high,producing a high output. As V_(in) continues to rise, however, it willbecome positive enough to overcome the negative bias at pin 4 of IC1.When this occurs, pin 4 will become positive with respect to pin 3, andIC1 output will go low. This in turn will cause AND gate output (pin 3of IC3) to go low.

The AND gate output (pin 3 of IC3) is thus high only when V_(in) isbetween the range between the small negative voltage and the smallpositive voltage. At all other times the AND gate output is low. The"window" of V_(in) voltages that produces a high output is determined bythe bias voltages set at pin 4 of IC1 by R9, and at pin 3 of IC2 by R7.It should be noted that when V_(in) decreases, the same result occurs.That is, when V_(in) goes below the window upper level (i.e. to somesmall positive voltage), pin 4 of IC1 will become more negative than pin3, giving a high output at IC1, and at IC3. But when V_(in) drops belowthe window lower level (i.e. beyond a small negative voltage), pin 3 ofIC2 will go negative, producing a low IC2 and IC3 output. The output ofAND gate IC3 is thus positive only when V_(in) transitions through thewindow of voltages set by R7 and R9.

The output of IC3 is voltage divided by Rll and potentiometer R12, andfiltered by capacitor C2. Output voltage, V_(out) is then applied to adigital multimeter (DMM) 14. DMM 14 effectively integrates the filteredoutput pulses from pin 3 of IC3. As explained above, IC3 will producepulse lengths equal to the amount of time that V_(in) is within thepreset window voltage range. DMM 14, therefore, reads a voltage that isproportional to the amount of time V_(in) is within this window. Putanother way, the DMM indicates the relative amount of time that an inputsignal is at a given input level range.

By setting R5 to make V_(x) some positive or negative value, the windowwill simply be raised or lowered. The window voltage range (i.e. thedifference between the window lower and upper voltage levels) remainsconstant. Therefore, R5 can be set for different values of V_(x), andDMM 14 will indicate the relative amount of time that the signal spendsat these levels. In practice, the window lower voltage, V_(L), andhigher voltage, V_(H), are set symmetrically about V_(x). The digitalmultimeter therefore indicates the relative amount of time that V_(in)equals V_(x), where V_(x) is approximated by a window of voltagesbetween V_(L) and V_(H).

This relationship is exactly what is given by theoretical probabilitydensity functions. That is, for Gaussian noise, the amplitudeprobability density function is: ##EQU1## where v is the instantaneousvoltage amplitude and s is the root mean square (rms) voltage level.This relationship is plotted on FIG. 3 for a value of s=140 mv rms, seeplot 16. The 140 mv rms value of s is a relatively arbitrary level,chosen in this case to be small enough for noise sources that wereactually tested, but high enough to be relatively insensitive to circuitfluctuations. The right hand ordinate of FIG. 3 is labeled as "V_(out)×10" since in this representative embodiment, the invention is normallycalibrated by R12 to give a DMM reading of 0.286 VDC with the 140 mv rmsnoise voltage in, with V_(x) set to 0 VDC. This makes measurementseasily related to the theoretical curve 16 (i.e. DMM reading times 10),while not requiring an additional amplifier with a gain of 10.

In practice the invention is easily calibrated by applying a sinewave ata frequency of about 4 kHz to the V_(in) input, and setting V_(x) equalto 0 VDC. The input signal, V_(in), and the output pulses at pin 3 ofIC3, V_(W), are simultaneously viewed on an instrument such as a dualtrace oscilloscope. Potentiometer R7 is then set so that the V_(W)pulses rise when V_(in) is at a -V_(L) level, and R9 is set so that thetrailing edge of V_(W) occurs when V_(in) is at a V_(H) level. Thisdefines the sampling window as V_(H) -V_(L), with V_(x) =0 VDC as theaverage value. Resistor R12 is then adjusted, as noted above, for 0.286VDC output with 140 mv rms of noise in. The area under the P(v) curve ofFIG. 3 between any two values of V_(x) represents the relativeprobability (or amount of time) that a signal voltage is within thewindowed voltage range. Therefore, for greatest accuracy, themeasurement window range should be as small as possible. However, verysmall window ranges can produce very low output voltages as well as highsensitivities to circuit imperfections. For practical purposes,therefore, with V_(x) =0 V, V_(L) can be set for -25 mv and V_(H) can beset for +25 mv, giving a 50 mv window range. This value has givenadequate accuracy for a number of commercial noise sources tested.

Once the invention has been calibrated as described above, measurementscan be done as follows. First, the noise source to be tested, signalsource 12, is connected to analyzer 10's V_(in) input. The output of thenoise source is adjusted for an amplitude of 140 mv rms, as read on atrue rms voltmeter. The value of V_(x) is then varied over the range,for example, -0.5 to +0.5 VDC, and V_(out) ×10 is recorded for eachvalue of V_(x) tested. By closely spacing the values of V_(x) continuousmeasurement resolution is possible. These measurements are plotted on agraph such as FIG. 3 so that measured curves can be directly compared totheoretical curve 16 for P(v). FIG. 3 shows examples of such test data.As can be seen, the measured values for a good noise source (shown as"X's) fall very closely to theoretical curve 16. However, the curve fora noise source known to be faulty (plotted with dots) shows a markeddeviation from Gaussian theory. This curve (18), indicates that thenoise signal contains inordinately high negative peaks, positive peakclipping, and a positively skewed, leptokurtic distribution. All ofthese non-Gaussian characteristics could be cross-correlated with anoscilloscope display of the signal. It should be noted that none ofthese characteristics would be readily visible from a cumulativeamplitude distribution of the faulty noise source.

As earlier discussed, the signal amplitude distribution analyzer of theinvention can also be used to measure cumulative amplitude distribution.This is done by setting switch S1 to the CUM position, therebydisconnecting the output from IC1 and connecting the pin 1 AND input ofIC3 to a high level of +5 VDC. This in effect makes IC3 just a bufferstage whose output is the same as the input of its pin 2. The circuit isthen recalibrated by first terminating the V_(in) input in 50 ohms (nosignal), setting V_(x) to some negative value, and setting R12 for a 1VDC DMM reading. Since IC2 and IC3 are both continuously high underthese conditions, simulating the case where V_(in) is always greaterthan 0 V, the 1 VDC DMM reading is set to indicate a 100% cumulativedistribution value. Next, with a noise source having an amplitude of 140mv rms connected to the V_(in) input, and with V_(x) set for 0 VDC, R7is set for a 0.5 VDC reading on the DMM. In this case, R7 acts only asan offset nulling adjustment for IC2, and the DMM reading indicates thatthe signal is above 0 VDC 50% of the time, as it should with V_(x) =0VDC.

Once calibrated, cumulative distribution measurement is made in the sameway as for other distribution measurements. The value of V_(x) is variedover a selected range such as 0 to +0.5 VDC and the cumulativedistribution is read on the DMM for a number of V_(x) values. Therecorded values of V_(x) and V_(out) (the left hand ordinate of FIG. 3)are then co-plotted with the theoretical Gaussian cumulativedistribution curve 20 as shown on the left of FIG. 3. In this casetheoretical curve 20 is defined by P(cum v), which is the integral ofthe distribution function from V_(x) to infinity. The P(cum v)theoretical curve 20 can also be computed using available tables and theformula: ##EQU2## where "erfc" is the complementary error function.

FIG. 3, in addition to showing distribution density function profiles,also shows cumulative distribution data obtained from the same noisesources tested for the distribution density function. Note that the goodnoise source (plotted as "X"s) produces test data points that lieclosely to theoretical curve 20. The faulty noise source data (shown asdots), on the other hand, departs from theoretical curve 20. However,unlike the data from distribution density function testing, littleindication is given as to the degree or character of this departure fromGaussianicity.

FIG. 3 provides a direct comparison of results from cumulative anddistribution density function testing. It shows how much more revealingit is to measure the distribution density function itself, rather thanto measure cumulative distribution, as is typically done. FIG. 3 alsoshows the measured amplitude distribution of a sinewave (22) forpositive values of V_(x). This demonstrates that the signal amplitudedistribution analyzer of the invention can be used to make amplitudedistribution measurements of any waveform type whether they berepetitive or non-repetitive.

The advantages of the signal amplitude distribution analyzer of theinvention over older methods of measuring signal amplitude distributionare many. The invention gives the capability of measuring probabilitydensity function itself rather than cumulative distribution functions,providing a more sensitive measure as to the degree of conformance of anoise source with theory. The invention is therefore capable ofcharacterizing deviations from theory rather than only indicating adegree of nonconformance.

As the invention is easily calibrated from a known input source, precisemeasurement of a signal source's deviations is possible. These sourcesmay be of a repetitive or non-repetitive type, with the inventionproviding a continuous, overlapping, resolution to enhance measurementaccuracy. The invention provides not only a mechanism to sense thepresence of sought-after signals, but also provides the relative amountof time that an input signal is within a selected signal range. Thislatter relationship is exactly what is given by theoretical probabilitydensity functions.

It should be noted that the signal amplitude distribution analyzer ofthe invention uses a very simple implementation scheme, requiring onlythree integrated circuit components. 0f course the invention could bemade more accurate by using more complex circuitry. It also could beimproved by using an analog-to-digital converter, computer interfacecircuits and computer analysis. The invention could also be expanded toprovide automatic threshold or window stepping, so that results could beprinted automatically on an X/Y recorder.

Obviously, many modifications and variations of the invention arepossible in light of the above teachings. It is therefore to beunderstood that within the scope of the appended claims the inventionmay be practiced otherwise than as has been specifically described.

What is claimed is:
 1. An apparatus for analyzing signals comprising:afirst comparator for comparing voltage of said signals to a preselectedlower voltage and for providing an output signal when the voltage ofsaid signals is above said preselected lower voltage; a secondcomparator for comparing voltage of said signals to a preselected highervoltage and for providing an output signal when the voltage of saidsignals is below said preselected higher voltage; and an AND circuitcoupled to said first and second comparators for providing a pulse uponsimultaneously receiving said output signals from said comparators, saidpulse having a pulse length corresponding to the elapsed time saidsignals are within a voltage window bounded by said lower and highervoltages.
 2. An apparatus according to claim 1 further including:anintegrator coupled to said AND circuit for integrating said pulseprovided by said AND circuit to provide a voltage proportional to saidelapsed time said signals are within said voltage window.
 3. Anapparatus according to claim 2 in which said integrator is a voltmeter.4. An apparatus according to claim 1 in which said apparatus iscalibrated by analyzing a known input signal.
 5. An apparatus accordingto claim 4 in which said known input signal is a Gaussian signal.
 6. Amethod for approximating the amplitude probability density distributionof signals comprising the steps of:comparing voltage of said signals toa preselected lower voltage in a first comparator; providing an outputsignal from said first comparator when the voltage of said signals isabove said preselected lower voltage; comparing voltage of said signalsto a preselected higher voltage in a second comparator; providing anoutput signal from said second comparator when the voltage of saidsignals is below said preselected higher voltage; providing a pulse froman AND circuit operably coupled to said first and second comparatorsupon said AND circuit simultaneously receiving said output signals fromsaid comparators, said pulse having a pulse length corresponding to theelapsed time said signals are within a voltage window bounded by saidlower and higher voltages; and integrating said pulse provided by saidAND circuit in an integrator to provide an output voltage proportionalto said elapsed time said signals are within said voltage window.
 7. Amethod according to claim 6 further including a step ofanalyzing a knowninput signal as a calibration of said comparators and said integrator.8. A method according to claim 7 in which said known input signal is aGaussian signal.
 9. A method according to claim 8 further includingsteps of:analyzing unknown input signals by shifting said voltage windowover a desired voltage range, each voltage window having a middlevoltage point; and plotting said output voltage versus said middlevoltage point for each voltage window examined.
 10. A method accordingto claim 9 further including the step of:comparing said plot to atheroretically derived probability density distribution to determine themagnitude of deviation of said plot from said theoretically derivedprobability density function.